create mesh then add vertices to it in python
This is how to create a new object and add the vertices in the verts list:

import bpy
import bmesh

verts = [(1, 1, 1), (0, 0, 0)]  # 2 verts made with XYZ coords
mesh = bpy.data.meshes.new("mesh")  # add a new mesh
obj = bpy.data.objects.new("MyObject", mesh)  # add a new object using the mesh

scene = bpy.context.scene
scene.objects.link(obj)  # put the object into the scene (link)
scene.objects.active = obj  # set as the active object in the scene
obj.select = True  # select object

mesh = bpy.context.object.data
bm = bmesh.new()

for v in verts:
    bm.verts.new(v)  # add a new vert

# make the bmesh the object's mesh
bm.to_mesh(mesh)  
bm.free()  # always do this when finished


This is how to alter an existing mesh:

import bpy
import bmesh

verts = [(1, 1, 1), (0, 0, 0)]  # 2 verts made with XYZ coords
mesh = bpy.context.object.data
bm = bmesh.new()

# convert the current mesh to a bmesh (must be in edit mode)
bpy.ops.object.mode_set(mode='EDIT')
bm.from_mesh(mesh)
bpy.ops.object.mode_set(mode='OBJECT')  # return to object mode

for v in verts:
    bm.verts.new(v)  # add a new vert

# make the bmesh the object's mesh
bm.to_mesh(mesh)  
bm.free()  # always do this when finished